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Modern pop culture would have us believe that there is such a thing as the 4th spatial dimension. And yes it's easily shown that $n$ dimensions is possible using math alone and 3 just happens to be our specific case. But as far as modern science goes, how confident are we that there are more than 3 spatial dimensions? Are there currently any accepted theories that rely on a 4th spacial dimension? (I'm particularly interested in this answer) I was provoked when I looked up how at the quantum level particles seem to pop in and out of existence. A simple write off that pop culture uses is that these particles are just "passing through" our 3D space as they travel fully through their higher dimensions. Is there much of a consensus on this?

Also please let's avoid discussion of time being the 4 dimension if at all possible. I'm speaking of space only.

Qmechanic
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RocketTwitch
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    possible duplicate of http://physics.stackexchange.com/q/208383/ http://physics.stackexchange.com/q/89988/ http://physics.stackexchange.com/q/104800/ – AccidentalFourierTransform Jan 03 '16 at 16:23
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    Related: http://physics.stackexchange.com/q/4079/2451 , http://physics.stackexchange.com/q/10527/2451 , http://physics.stackexchange.com/q/31882/2451 and links therein. – Qmechanic Jan 03 '16 at 16:28
  • not so duplicate : it is the only question with the image of virtual particles poping in and out of existence . It is a specific argument to refute or comment –  Jan 03 '16 at 19:53
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    Particles do not pop in and out of existence. That, too, is just a pop-science version of quantum field theory. Even the existence of particles is pop-science, although on such a high level that even colleagues are sometimes still emotionally attached to that notion. – CuriousOne Jan 04 '16 at 09:48

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